A307292 -id:A307292 - cp's OEIS frontend

A307290 Number of black-and-white colored (or proper magnetic) space groups in dimension n, counting enantiomorphs.

Original entry on oeis.org

0, 3, 46, 1191, 52439

Offset: 0

N. J. A. Sloane, Apr 08 2019

R. L. E. Schwarzenberger, Colour symmetry, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.
B. Souvignier, Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6, Acta Cryst., A59 (2003), 210-220.

Cf. A006227, A307291, A307292.

a(n) = A307291(n) - 2 * A006227(n). - Andrey Zabolotskiy, Apr 09 2019

a(0), a(4) from Andrey Zabolotskiy, Apr 09 2019

A307293 Number of color plane groups of index n.

Original entry on oeis.org

17, 46, 23, 96, 14, 90, 15, 166, 40, 75, 13, 219, 16, 80, 34, 262, 14, 174, 15, 205, 38, 88, 13, 433, 31, 103, 48, 222, 14, 213, 15, 395, 36, 111, 24, 452, 16, 116, 40, 416, 14, 250, 15, 265, 62, 124, 13, 741, 32, 193, 38, 300, 14, 303, 24, 468, 42, 147, 13, 627, 16

Offset: 1

N. J. A. Sloane, Apr 08 2019

nonn

			a(1) = A004029(2), a(2) = A307292(2).

Branko Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987, chapter 8 "Colored patterns and tilings".
Thomas W. Wieting, The Mathematical Theory of Chromatic Plane Ornaments, Marcel Dekker, Inc., 1982. See Table 11 at pages 250-254.

R. L. E. Schwarzenberger, Colour symmetry: Part two, Bulletin of the London Mathematical Society 16.3 (1984): 216-229. See page 221.
R. L. E. Schwarzenberger, Review of "The Mathematical Theory of Chromatic Plane Ornaments" by Thomas W. Wieting, Bull. London Math. Soc., 15 (1983), 163-164.
Marjorie Senechal, Color groups, Discrete Applied Mathematics, 1 (1979), 51-73.

Cf. A004029, A307292.

a(p) = 16, 15, 14, 13 if p == 1, 7, 5, 11 (mod 12), respectively, and a(p^2) = a(p) + 17, where p is a prime greater than 3. These formulas are found by Senechal. Schwarzenberger (1983) says that her results are correct for these cases, while some other results have essentially been corrected by Wieting. - Andrey Zabolotskiy, May 18 2022

a(1) and a(16)-a(60) from Wieting added by Andrey Zabolotskiy, Apr 09 2019

a(61) added by Andrey Zabolotskiy, May 18 2022

cp's OEIS Frontend

A307290 Number of black-and-white colored (or proper magnetic) space groups in dimension n, counting enantiomorphs.

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